Derived and prismatic F-Zips (C03)

• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444845124

The project aims to study the total de Rham cohomology of proper syntomic morphisms in positive characteristic p > 0 and, more generally, over certain p-adically complete bases. The goal is to endow the total de Rham cohomology with additional structures extending those of an F-zip to obtain the notion of a derived F-zip. We want to study moduli spaces of derived F-zips to obtain mod p period spaces. These moduli spaces will be locally geometric derived stacks and we plan to study their structure and in particular their singularities. We also plan to study variants for log-syntomic morphisms. Using the pris¬matic cohomology we plan to extend these results in order to obtain mixed characteristic period spaces.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 326: Geometry and Arithmetic of Uniformized Structures (GAUS)
• Applicant Institution: Goethe-Universität Frankfurt am Main
• Project Heads: Professor Dr. Manuel Blickle, Ph.D.; Professor Dr. Torsten Wedhorn